Jambo, Bwana!
Let's take the simplest first:
Double action only: There is no safety or decocking lever. The safety is provided by the longer, heavier trigger pull, just like a DA revolver. After firing, the pistol does not stay cocked. You have to go through the long pull again to fire another.
Pros: simple, no need top remember to push levers. Fewer doohickeys to go wrong (though a mechanical failure in a Ruger is rarer than an uneaten donut in a police station). Cons: Tired trigger finger, and it's harder to make precision shots with a DAO.
Decock only: It has a lever on the slide. The first shot is a long, heavy trigger pull, and when the slide cycles, the hammer stays back for the next shot. This gives a light, short trigger pull for subsequent shots. The lever is not a true "safety", it just lowers the hammer without firing the gun ,so you're back in the same starting long-hard trigger pull mode. The lever is spring loaded, and after decocking returns to the starting position.
Pros: After first shot, it's easier to make accurate, rapid follow ups. Cons: Have to get used to two trigger pulls, and if you forget to decock before holstering you can blow half your butt off.
Manual safety: The lever is a true safety, blocking the firing mechanism. It must be moved from Safe to Fire before you shoot. Otherwise, it works like the decocker version.
Pros: If you want to carry Condition One, cocked and locked, you can have the same light pull for all shots. Also, if you can switch it on before a bad guy disarms you, it may take him long enough to figure out the safety that you can disable him with your backup gun, folding knife or a good swift kick to the gonads. Cons: Most complex manual of arms. In stress situations if you're in Condition One, you may press the lever too far and decock. If you forget to decock or put it back on safe, you can still shoot yourself in the butt while holstering.
Which you choose is a matter of personal preference, and that's cool so long as you take the trouble to learn your manual of arms. I like the decocker (I own a P95) but for a newbie defensive shooter or someone who's not going to practice much I would suggest the DAO.